First slide

Introduction to waves

Question

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the waves are :

Moderate

A

1, 2, 3, .....
B

$\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, .....$
C

1, 3, 5, .....
D

$\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, .....$

Solution

Distance between crests $= n λ = 5$
So $λ = \frac{5}{n} m ........ (1)$
Also distance between a crest and trough is given as 1.5 m

$\Rightarrow (2 k - 1) \frac{λ}{2} = 1.5$
So $λ = \frac{3}{2 k - 1} ....... (2)$
$(1), (2)$ satisfy, $\frac{n}{2 k - 1} = \frac{5}{3} = \frac{15}{9} = \frac{25}{15}$
$\Rightarrow n \in \{5, 15, 25, .......\}$
So $λ \in \{1, \frac{1}{3}, \frac{1}{5}, ........\}$

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